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A trinomial tree method for pricing path-dependent options in a eneralized jump-diffusion model

Title
A trinomial tree method for pricing path-dependent options in a eneralized jump-diffusion model
Authors
LiuYiwen
Date Issued
2012
Publisher
포항공과대학교
Abstract
Option contracts have become increasingly important in the field of finance since they possess characteristics that are attractive to speculators and hedgers. One important problem is determining the ”fair value” of an option efficiently and accurately. In this thesis, we review some basic option pricing theories. After discussing some popular numerical methods for option pricing, we focus on dealing with path dependent options. We first propose a generalized parabolic integro differential equation (PIDE) model for pricing path-dependent options with jumps. Since the PIDE model does not have a closed-form solution, in order to know the approximate solution, we present a trinomial tree method instead of the traditional binomial tree method and show its consistence with our proposed PIDE model. We also give an explicit finite difference scheme and show its equivalence to the trinomial tree scheme. Therefore we prove the uniform convergence of the trinomial tree method for European-style path dependent options with jumps. Further, comparison studies are performed to demonstrate the advantages of the trinomial tree method over the binomial tree method for pricing European put options computationally.
URI
http://postech.dcollection.net/jsp/common/DcLoOrgPer.jsp?sItemId=000001217042
http://oasis.postech.ac.kr/handle/2014.oak/1412
Article Type
Thesis
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